determine the max interval on which the solution is defined

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I need help in this problem

consider the following IVP :

$$y' = y^2 + e^{-x^2}, \; y(0) = 0$$

now I've tried to solve this equation by first solving the associated homogeneous equation which gives : $$y(x) ={-1\over x+K}$$

then by the method of variation of parameters I ended up with this equation : $$ {K'(x)\over (x+K^2(x))} =e^{-x^2}$$

which I don't think I could get anywhere from it